{"paper":{"title":"Collision Resistance of Single-Layer Neural Nets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"cs.CR","authors_text":"Alon Rosen, Andrej Bogdanov, Enrico M. Malatesta, Gianmarco Perrupato, Marc M\\'ezard, Marco Benedetti, Nikolaj I. Schwartzbach, Riccardo Zecchina","submitted_at":"2026-06-02T15:52:45Z","abstract_excerpt":"We initiate the study of the algorithmic complexity of finding collisions in single-layer binary neural networks. Given a random matrix $\\mathbf{A} \\in \\mathbb{R}^{m\\times n}$, an input $\\mathbf{x} \\in \\{-1,1\\}^n$ is mapped to a binary output vector $\\varphi(\\mathbf{A}\\mathbf{x})\\in \\{-1,1\\}^m$, where $\\varphi$ is an activation function with constant behavior on $[\\kappa, \\infty)$ for some threshold $\\kappa \\geq 0$.\n  We identify the threshold scale $\\kappa=\\Theta(1/\\sqrt{\\alpha})$, where $\\alpha=m/n$, as separating two complementary phenomena. When $\\kappa \\ll 1/\\sqrt{\\alpha}$, we give a simp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.03807","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.03807/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}